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Centre for Quantum Information and Foundations

 

IB Quantum Mechanics

Lecturer: Adrian Kent
Michaelmas Term 2019, 16 lectures, Tuesday, Thursday at 11am in Mill Lane lecture room 3

Course materials

Introductory summary

Full lecture notes (minor corrections 31.12.19 and 16.05.20)

Lecture notes part 1 (completed)

Lecture notes part 2 (completed)

Lecture notes part 3 (completed)

Lecture notes part 4 (completed)

Lecture notes part 5

Example sheet 1

Example sheet 2

Example sheet 3

Slides on fission, fusion and the tunnelling electron microscope (non-examinable)

Slides on existence and uniqueness of hermitian conjugate (non-examinable)

Slides on why position and momentum measurements are approximate (non-examinable)

Slide on measurement of a degenerate eigenvalue

Slides on photon polarization measurements (non-examinable)

Slide on uncertainty and statistical variance

Slides for lecture 12 (uncertainty, Ehrenfest, harmonic oscillator)

Slides for lecture 13 (QM in 3D; central potentials)

Slides for lecture 14 (Hydrogen atom spherically symmetric states; angular momentum)

Slides for lecture 15 (Full solution of Hydrogen atom)

Links to resources

Research suggests that students learning quantum mechanics for the
first time encounter similar problems and temporary confusions.
This seems to be true for students with a wide range of backgrounds
and aptitudes. The article below discusses some points where
confusion often arises: you may want to test yourself on the
questions. It also gives links to a range of simulation tools
designed to build and test intuitions about quantum mechanics.

https://physicstoday.scitation.org/doi/10.1063/1.2349732

Double slit experiment

Tonomura's double slit experiment is discussed here, with a link to the narrated video:

https://www.hitachi.com/rd/portal/highlight/quantum/doubleslit/index.html

Arndt's group's experiments on large molecule interferometry are described here:

https://www.quantumnano.at/

A simulation of a wave packet in a double slit experiment is here:

https://www.youtube.com/watch?v=jHyO0A7C86E

Gaussian wave packets

A nice discussion of some of their properties, with simulations, is at:

https://www.cond-mat.de/teaching/QM/JSim/wpack.html

Scattering and tunnelling

Simulations of wavepacket scattering from various potentials can be found at

https://www.youtube.com/watch?v=mmLDtkpg3wQ

(near perfect reflection from a square potential with U>>E)

https://www.youtube.com/watch?v=TQIMQzw_-lQ

(scattering and transmission from a step potential: note that

the wavelength of the transmitted wave is longer, because

it loses some momentum in climbing the potential step.

This simulation gives a clear picture of wavepacket reflection and

transmission up to about 0.06; reflecting endpoint boundary

conditions confuse the picture after that.)

Scattering of a 2D wave packet from a potential:

https://www.youtube.com/watch?v=8qOXof9_34M

Simulations of reflection from and tunnelling through a square potential barrier

can be found at

https://www.youtube.com/watch?v=4-PO-RHQsFA

https://www.youtube.com/watch?v=_3wFXHwRP4s

Lecture notes part 4 (completed)Reflection from and tunnelling through square potential well and barrier:

https://www.youtube.com/watch?v=cV2fkDscwvY

A nice review of the significance of tunnelling in some chemical reactions:

https://science.sciencemag.org/content/299/5608/833

Ehrenfest's theorem

Illustration of a Gaussian wave packet in the harmonic oscillator potential:

https://www.youtube.com/watch?v=1fMi1nriS8Q